22 research outputs found
Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber
The present investigation deals with the dynamics of a two-degrees-of-freedom
system which consists of a main linear oscillator and a strongly nonlinear
absorber with small mass. The nonlinear oscillator has a softening hysteretic
characteristic represented by a Bouc-Wen model. The periodic solutions of this
system are studied and their calcu- lation is performed through an averaging
procedure. The study of nonlinear modes and their stability shows, under
specific conditions, the existence of localization which is responsible for a
passive irreversible energy transfer from the linear oscillator to the
nonlinear one. The dissipative effect of the nonlinearity appears to play an
important role in the energy transfer phenomenon and some design criteria can
be drawn regarding this parameter among others to optimize this energy
transfer. The free transient response is investigated and it is shown that the
energy transfer appears when the energy input is sufficient in accordance with
the predictions from the nonlinear modes. Finally, the steady-state forced
response of the system is investigated. When the input of energy is sufficient,
the resonant response (close to nonlinear modes) experiences localization of
the vibrations in the nonlinear absorber and jump phenomena
Forced and self-excited oscillations of an optomechanical cavity
We experimentally study forced and self oscillations of an optomechanical
cavity which is formed between a fiber Bragg grating that serves as a static
mirror and between a freely suspended metallic mechanical resonator that serves
as a moving mirror. In the domain of small amplitude mechanical oscillations,
we find that the optomechanical coupling is manifested as changes in the
effective resonance frequency, damping rate and cubic nonlinearity of the
mechanical resonator. Moreover, self oscillations of the micromechanical mirror
are observed above a certain optical power threshold. A comparison between the
experimental results and a theoretical model that we have recently presented
yields a good agreement. The comparison also indicates that the dominant
optomechanical coupling mechanism is the heating of the metallic mirror due to
optical absorption.Comment: 11 pages, 6 figure
Cascades of subharmonic stationary states in strongly non-linear driven planar systems
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial
non-linearity subjected to an external periodic excitation is studied. The
sequences (cascades) of harmonic and subharmonic stationary solutions to the
equation of motion are obtained by using the harmonic balance approximation
adapted for arbitrary truncation numbers, powers of non-linearity, and orders
of subharmonics. A scheme for investigating the stability of the harmonic
balance stationary solutions of such a general form is developed on the basis
of the Floquet theorem. Besides establishing the stable/unstable nature of a
stationary solution, its stability analysis allows obtaining the regions of
parameters, where symmetry-breaking and period-doubling bifurcations occur.
Thus, for period-doubling cascades, each unstable stationary solution is used
as a base solution for finding a subsequent stationary state in a cascade. The
procedure is repeated until this stationary state becomes stable provided that
a stable solution can finally be achieved. The proposed technique is applied to
calculate the sequences of subharmonic stationary states in driven hardening
Duffing's oscillator. The existence of stable subharmonic motions found is
confirmed by solving the differential equation of motion numerically by means
of a time-difference method, with initial conditions being supplied by the
harmonic balance approximation.Comment: 37 pages, 11 figures, revised material on chaotic motio
Qualitative Analysis of Forced Response of Blisks With Friction Ring Dampers
A damping strategy for blisks (integrally bladed disks) of turbomachinery
involving a friction ring is investigated. These rings, located in grooves
underside the wheel of the blisks, are held in contact by centrifugal loads and
the energy is dissipated when relative motions between the ring and the disk
occur. A representative lumped parameter model of the system is introduced and
the steady-state nonlinear response is derived using a multi-harmonic balance
method combined with an AFT procedure where the friction force is calculated in
the time domain. Numerical simulations are presented for several damper
characteristics and several excitation configurations. From these results, the
performance of this damping strategy is discussed and some design guidelines
are given